1. The problem statement, all variables and given/known data Find the values of a and b that make f a differentiable function. Note: F(x) is a piecewise function f(x): Ax^2 - Bx, X ≤ 1 Alnx + B, X > 1 2. Relevant equations 3. The attempt at a solution Made the two equations equal each other. Ax^2 - Bx = Alnx + B Inserting x=1 gives, A - B = B, which is also A - 2B = 0, which also means A = 2B Deriving the equation, 2Ax - B = A/X Inserting x=1 here gives, 2A - B = A, which is also A - B = 0, which also means A = B By then I'm stumped here. I try to eliminate either A and B with, A - B = 0 A - 2B = 0 In the end, both A and B would have to equal zero, both of which doesn't work. If I have A = 2B then, F'(x): A - B = 0 ⇒ 2B - B = 0 ⇒ B = 0 As said before, B = 0 would not be the right answer, as far as I know at least. If A = B, then F(x): A - 2B = 0 ⇒ B - 2B = 0 ⇒ B = 0 Once Again, B equaling zero would not work. Right now, i'm convinced this problem is virtually impossible.